What are decimal numbers?
Decimal numbers are numbers that have a whole part and a fractional part separated by a decimal point. The decimal point looks like a small dot (.). Digits to the left of the decimal point are whole numbers. Digits to the right show parts of a whole, such as tenths or hundredths.
- 3.42 — The whole part is 3. The fractional part is 42 hundredths.
- 15.07 — The whole part is 15. The fractional part is 7 hundredths.
- 0.89 — The whole part is 0. The fractional part is 89 hundredths.
In fourth grade, you will work with decimals to the tenths (one digit after the decimal) and hundredths (two digits after the decimal). Always line up the decimal points when adding or subtracting.
Adding decimals: the rule of lining up decimal points
To add decimals correctly, write the numbers in a vertical column so that the decimal points are directly above each other. Then add each place value column starting from the rightmost digit (hundredths), just like adding whole numbers. Bring the decimal point straight down into your answer.
- Step 1: Write the numbers with decimal points lined up.
- Step 2: Add hundredths: 2 + 8 = 10. Write 0 in the hundredths place, carry 1 to the tenths place.
- Step 3: Add tenths: 4 + 5 + carry 1 = 10. Write 0 in the tenths place, carry 1 to the ones place.
- Step 4: Add ones: 8 + 1 + carry 1 = 10. Write 0 in the ones place, carry 1 to the tens place.
- Step 5: Add tens: 3 + 2 + carry 1 = 6. Write 6 in the tens place.
- Step 6: Bring the decimal point straight down between the ones and tenths.
The sum is 60.00, which is the same as 60.
If a decimal does not show a decimal point, you can add one at the end. For example, 7 is the same as 7.00. This helps you line up the numbers correctly.
Adding decimals with different numbers of digits
Sometimes the decimals you add do not have the same number of digits after the decimal point. To fix this, add zeros to the right of the shorter decimal until both have the same number of decimal places. Adding zeros does not change the value of the number.
- Step 1: Write 5.3 as 5.30 (add one zero to make hundredths).
- Step 2: Line up decimal points.
- Step 3: Add hundredths: 0 + 7 = 7.
- Step 4: Add tenths: 3 + 4 = 7.
- Step 5: Add ones: 5 + 2 = 7.
- Step 6: Add tens: 0 + 1 = 1.
The sum is 17.77.
Always write the numbers so that the decimal points are in a straight vertical line. If you forget the zeros, you might add tenths to hundredths incorrectly.
Subtracting decimals: the same lining-up rule
Subtracting decimals follows the same first rule as adding: line up the decimal points. Then subtract each column starting from the rightmost digit. If a column does not have enough digits, use zeros as placeholders. Borrow from the left when needed, just like subtracting whole numbers.
- Step 1: Line up decimal points.
- Step 2: Subtract hundredths: 7 – 4 = 3.
- Step 3: Subtract tenths: 6 – 3 = 3.
- Step 4: Subtract ones: 5 – 2 = 3.
- Step 5: Subtract tens: 4 – 1 = 3.
The difference is 33.33.
Never forget to bring the decimal point straight down into your answer. If you leave it out, the answer will look like a whole number and will be wrong.
Subtracting decimals when borrowing is needed
Sometimes a digit in the top number is smaller than the digit directly below it. When that happens, you must borrow 1 from the next left column. The 1 you borrow becomes 10 in the smaller column because of the decimal place value.
- Step 1: Line up decimal points. Write 52.03 and 17.28.
- Step 2: Hundredths: 3 is less than 8. Borrow 1 tenth from the 0 tenths? The 0 tenths has nothing to borrow, so borrow 1 one from the 2 ones. That 1 one becomes 10 tenths. Then borrow 1 tenth from those 10 tenths to give 10 hundredths. Now hundredths: 13 – 8 = 5.
- Step 3: Tenths: after borrowing, 9 tenths remain. 9 – 2 = 7.
- Step 4: Ones: after borrowing, 1 one remains. 1 – 7? It cannot be. Borrow 1 ten from 5 tens. That 1 ten becomes 10 ones. Now ones: 11 – 7 = 4.
- Step 5: Tens: 4 tens remain. 4 – 1 = 3.
The difference is 34.75.
Borrowing across zeros can be tricky. Remember that every time you borrow, the number to the left decreases by 1, and the number you are borrowing for increases by 10.
Checking your work with inverse operations
After you add or subtract decimals, you can check if your answer is correct by using the opposite operation. For addition, subtract one of the addends from the sum. You should get the other addend. For subtraction, add the difference to the smaller number. You should get the larger number.
Check by subtraction: 60.00 – 21.58 should equal 38.42.
The check works, so the original addition is correct.
Check by addition: 34.75 + 17.28 should equal 52.03.
The check works, so the subtraction is correct.
Checking your work takes only a few extra seconds and helps you catch mistakes before you turn in your assignment.
Adding and subtracting decimals in word problems
In real life, decimals appear in money (dollars and cents), distances (kilometers and meters), weights (kilograms and grams), etc. The key to solving word problems is to identify which numbers to add or subtract and then line up the decimal points carefully.
Add: $4.75 + $1.25
Maria spent $6.00.
Subtract: $20.00 – $12.99
Kevin has $7.01 left.
When a word problem gives whole dollar amounts like $5, write them as $5.00 before adding or subtracting. This keeps your decimal points lined up.
Common mistakes to avoid
Even careful students sometimes make predictable mistakes with decimals. Knowing these mistakes in advance helps you avoid them.
Wrong way: Adding 4.5 + 3.27 by writing 4.5 + 3.27 without zeros. This puts tenths under hundredths.
This is incorrect because the decimal points are not aligned. The correct way: Write 4.5 as 4.50, then add.
Aligning decimal points prevents place value errors that would occur with other numbers.
Subtracting 5.00 – 2.34: Some students say 0 – 4 cannot be done, so they guess. The correct borrowing gives 4.66.
Adding 12.5 + 7.5 = 20.0, not 200. The decimal point matters.
Slow down and check your alignment. Most decimal errors come from rushing past the decimal point.
Estimating before you add or subtract decimals
Estimation helps you know if your exact answer is reasonable. Round each decimal to the nearest whole number, then add or subtract. Your exact answer should be close to the estimate.
Round 38.42 to 38. Round 21.58 to 22. Estimate: 38 + 22 = 60. Exact answer: 60.00. The estimate matches exactly.
Round 52.03 to 52. Round 17.28 to 17. Estimate: 52 – 17 = 35. Exact answer: 34.75. The estimate is very close (35 vs. 34.75).
If your exact answer is far from your estimate, you likely made a calculation error. Go back and check your work.
Common Core alignment: CCSS.MATH.CONTENT.4.NBT.B.4 – Fluently add and subtract multi-digit whole numbers using the standard algorithm. (Extends to decimals to hundredths as foundational work for 5.NBT.B.7)
Notes for teachers
This lesson is aligned with CCSS.MATH.CONTENT.4.NBT.B.4 and supports the Grade 4 Number & Operations in Base Ten cluster. It introduces decimal addition and subtraction with a focus on place value, lining up decimal points, and borrowing across zeros. All content is 100% free, use it for whole-class instruction, independent study and practice, or homework.